Skip to main content
SpringerLink
Log in

Reasoning in Paraconsistent Logics

  • Chapter
Automated Reasoning

Part of the book series: Automated Reasoning Series ((ARSE,volume 1))

Abstract

Databases and knowledge bases could be inconsistent in many ways. For example, if a programmer is constructing an expert system ES relating to a domain D,he does so by consulting several experts (say n in number) in the field D. From each expert d i , 1 ≤ i ≤ n, he obtains some information, and this may be represented in logic as a collection of sentences, ES i , for 1 ≤ i ≤ n. The simplest way of combining the resulting knowledge is to set

$$ ES = \bigcup\limits_{i = 1}^n {ES_i .} $$

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Anderson and W. W. Bledsoe (1970): A Linear Format for Resolution with Merging and a New Technique for Establishing Completeness. JACM 17(3), 525–534.

    Article  MathSciNet  MATH  Google Scholar 

  2. N. D. Belnap (1977): A Useful Four-Valued Logic. In: G. Epstein and J. M. Dunn, eds.: Modern Uses of Many-valued Logic. D. Reidel, 8–37.

    Google Scholar 

  3. H. A. Blair and V. S. Subrahmanian (1987): Paraconsistent Logic Programming. Proc. 7th Conference on Foundations of Software Technology and Theoretical Computer Science. Lecture Notes in Computer Science 287, 340–360, Springer Verlag. Extended version in: Theoretical Computer Science 68, 135–154.

    Google Scholar 

  4. H. A. Blair and V. S. Subrahmanian (1988): Paraconsiistent Foundations for Logic Programming. Journal of Non-Classical Logic 5(2), 45–73.

    MathSciNet  Google Scholar 

  5. C. L. Chang and R. C. T. Lee (1973): Symbolic Logic and Mechanical Theorem Proving. Academic Press.

    MATH  Google Scholar 

  6. P. D. Cheng and J. Y. Juang (1987): A Parallel Resolution Procedure Based on Connection Graph. Proc. Sixth AAAI, 13–17.

    Google Scholar 

  7. N. C. A. da Costa (1974): On the Theory of Inconsistent Formal Systems. Notre Dame J. of Formal Logic 15, 497–510.

    Article  MATH  Google Scholar 

  8. N. C. A. da Costa and E. H. Alves (1981): Relations between Paraconsistent Logic and Many-valued Logic. Bulletin of the Section of Logic 10, 185–191.

    MATH  Google Scholar 

  9. N. C. A. da Costa, J. J. Lu, V. S. Subrahmanian, and L. J. Henschen (1989): Automatic Theorem Proving in Paraconsistent Logics: Foundations and Experimental Results. Proc. 10th CADE, LNCS, Springer Verlag, 72–86.

    Google Scholar 

  10. N. C. A. da Costa, V. S. Subrahmanian, and C. Vago (1989): The Paraconsistent Logics PT. to appear in: Zeitschrift fur Mathematische Logik and Grundlagen der Mathematik, 37, 1991.

    Google Scholar 

  11. B. A. Davey and H. A. Priestley (1990): Introduction to Lattices and Order. Cambridge University Press.

    MATH  Google Scholar 

  12. M. C. Fitting (1989): Bilattices and the Theory of Truth. Journal of Philosophical Logic 18, 225–256.

    Article  MathSciNet  MATH  Google Scholar 

  13. M. C. Fitting (1988): Logic Programming on a Topological Bilattice. Fundamenta Informatica 11, 209–218.

    MathSciNet  MATH  Google Scholar 

  14. M. C. Fitting (1988): Bilattices and the Semantics of Logic Programming. To appear in: Journal of Logic Programming.

    Google Scholar 

  15. D. Fishman and J. Minker (1975): 1-Representation: A Clause Representation for Parallel Search. Artificial Intelligence 6, 103–127.

    Article  MathSciNet  MATH  Google Scholar 

  16. M. Kifer and T. Krishnaprasad (1989): An Evidence Based Framework for a Theory of Inheritance. Proc. 11th International Joint Conf. on Artificial Intelligence, 1093–1098.

    Google Scholar 

  17. M. Kifer and E. Lozinskii (1989): RI: A Logic for Reasoning with Inconsistency. LICS-89.

    Google Scholar 

  18. M. Kifer and J. Wu (1989): A Logic for Object Oriented Logic Programming. Proc. 8th ACM Symp. on Principles of Database Systems, 379–393.

    Google Scholar 

  19. D. W. Loveland (1970): A Linear Format for Resolution. Proc. IRIA Symp. on Automatic Demonstration, Lecture Notes in Mathematics, Springer, 147–162.

    Google Scholar 

  20. D. W. Loveland (1972): A Unifying View of some Linear Herbrand Procedures. JACM 19, 366–384.

    Article  MathSciNet  MATH  Google Scholar 

  21. J. J. Lu, L. J. Henschen, V. S. Subrahmanian and N. C. A. da Costa (1990): Automated Deduction in Paraconsistent Logics. The full version of this paper. Tech Report, Northwestern University.

    Google Scholar 

  22. J. Roberge (1988): Distributed Resolution-based Theorem Proving Systems. Ph. D. Thesis, Northwestern University.

    Google Scholar 

  23. V. S. Subrahmanian (1987): On the Semantics of Quantitative Logic Programs. Proc. 4th IEEE Symposium on Logic Programming, Computer Society Press, Washington DC, 173–182.

    Google Scholar 

  24. V. S. Subrahmanian (1989): Algebraic Properties of the Space of Multivalued and Paraconsistent Logic Programs. Proc. 9th Intl. Conf. on Foundations of Software Technology and Theoretical Computer Science, LNCS 405, Springer-Verlag, 56–67.

    Google Scholar 

  25. L. Wos, D. Carson, and G. Robinson (1964): The Unit Preference Strategy in Theorem Proving. Proceedings of the AFIPS Conference 26, 615–621.

    Google Scholar 

  26. L. Wos (1988): Automated Reasoning: 33 Research Problems. Prentice Hall.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Northwestern University, Evanston, Illinois, USA

    James J. Lu & Lawrence J. Henschen

  2. University of Maryland, College Park, Maryland, USA

    V. S. Subrahmanian

  3. University of Sao Paulo, Brazil

    Newton C. A. da Costa

Authors
  1. James J. Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lawrence J. Henschen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. S. Subrahmanian
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Newton C. A. da Costa
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Computer Sciences Department, University of Texas at Austin, USA

    Robert S. Boyer

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Lu, J.J., Henschen, L.J., Subrahmanian, V.S., da Costa, N.C.A. (1991). Reasoning in Paraconsistent Logics. In: Boyer, R.S. (eds) Automated Reasoning. Automated Reasoning Series, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3488-0_9

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-3488-0_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5542-0

  • Online ISBN: 978-94-011-3488-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation